Single-use beverage cups or cartridges typically contain a dry beverage product such as coffee grounds, tea leaves, or a dry beverage concentrate (e.g. freeze-dried coffee crystals) or the like, such as for use in single-serving beverage brewing machines. Depending on the type of beverage product the cartridge contains, the cartridge may include a filter to prevent particles of beverage product from exiting the cartridge during a beverage-making operation. Such beverage cartridges are typically pierced in one or more locations to inject water and to drain a resulting prepared beverage out of the cartridge and into a receptacle.